I would love this. It supports brainstorming-type scenarios as well as situations where the poll creator overlooked something. It’s also useful for “suggestion box” type polls.
I’ve seen the “why this is a bad idea” posts, and I understand the “have a discussion first then make a static poll” advice, but whilst I respect your opinions, you are quite wrong. I’ve used similar open polls in other communities with great success. Yes, later options will get less votes, but that’s fine. We’re not trying to elect the leader of a nation — I just want to get gather some ideas from forum users.
Limiting added suggestions to one per user would make sense.
And of course there should be the option to disable user-added options.